MP Police Constable : (3 Nov 2025, Shift 1) Memory-Based Paper (Previous Year Paper)

The correct option is 2 i.e., Electoral system.

• Articles 324 to 329 in Part XV of the Constitution of India deals with the Electoral system of India.
• The Election Commission of India is an autonomous constitutional authority.
• The Election Commission was established on 25^th January 1950.
• The President appoints Chief Election Commissioner and Election Commissioners.
• Chief Election Commissioner a fixed tenure of six years, or up to the age of 65 years, whichever is earlier.

The correct answer is Newton’s third law of motion.

Key Points

• When a ball drops on the floor it bounces.
• This is according to Newton’s third law of motion.

Additional Information 

• Newton's third law implies that for every action there is a reaction.
• When a ball drops on to the floor it bounces because
• As Newton's third law implies that for every action there is a reaction.

Let 100x be the total salaried population in the city.

60% of salaried population in the city is working in a private sector = 60x

Therefore population working in government sector = 40x

Male members in private sector = 40% of 60x ⇒ 24x

Female members in private sector = 60% of 60x ⇒ 36x

40% of government sector employees are females = 40% of 40x ⇒ 16x

Therefore Male members working in government sector ⇒ 24x

Inference: I) Number of men working in private sector is equal to number of men working in government sector → True (as number of men working in private sector = 24x and number of men working in government sector = 24x)

Inference: II) Population of working women in the city is 60 % of the total salaried population → False

(as total working women are = (Female members in private sector is 36x + Female members in government sector is 16x = 52x) not 60% of total salaried population)

Hence, Only Inference I follows.

Given:

The ratio of the heights of a right circular cone and a right circular cylinder is 4 : 3.

The ratio of the radii of their bases is 7 : 3.

The volume of the cylinder is 810 cm³.

Formula used:

Volume of a cone, V_cone = (1/3)πr²h

Volume of a cylinder, V_cylinder = πr²h

Calculations:

Let the height of the cone be 4x and the height of the cylinder be 3x.

Let the radius of the cone be 7y and the radius of the cylinder be 3y.

Volume of the cylinder, V_cylinder = π(3y)²(3x)

Given V_cylinder = 810 cm³

⇒ π(9y²)(3x) = 810

⇒ 27πxy² = 810

⇒ xy² = 30/π

Volume of the cone, V_cone = (1/3)π(7y)²(4x)

⇒ V_cone = (1/3)π(49y²)(4x)

⇒ V_cone = (196/3)πxy²

⇒ V_cone = (196/3)π(30/π)

⇒ V_cone = 1960

∴ The correct answer is option 1.

The logic followed here is:

So, '133' will complete the series.

Hence, the correct answer is "Option 3".

Given:

A and B together can do a piece of work in 8 days.

A alone can do this work in 12 days

Formula used :

Efficiency = Work/Day

Calculation:

Total work = L C M of (8, 12 ) = 24 

Efficiency of A + B = 24/8  = 3

Efficiency of A = 24/12 = 2 

Efficiency of B = 3 - 2 = 1

Time taken by B alone = 24 days.

The answer is 24 days.

The correct answer is Road.

Key Points

• The Bharatmala project envisions improving the efficiency of the National Corridor including the Golden-Quadrilateral and North, South–East West corridors.
• It is trying to decongest the choke points through the construction of elevated corridors, bypasses, ring roads, lane expansion, and logistics parks at identified points.
• A total of 225 road projects with an aggregate length of 9,613 km have been appraised and approved till March 2019 under Bharatmala Pariyojana.

Additional Information

• Sagarmala Programme
• It is an initiative by the Government of India to enhance the performance of the country's logistics sector.
• The programme envisages unlocking the potential of waterways and the coastline to minimize infrastructural investments required to meet these targets.

The correct answer is Instantaneous velocity.

Key Points

• Instantaneous velocity:
• It is defined as the velocity of an object under motion at any given instant of time. So, option 1 is correct.
• The SI unit of instantaneous velocity is m/s.
• The average velocity of an object is defined as its total displacement divided by the total time taken.
• Variable velocity is defined as the change of velocity with time.
• Uniform velocity: A body is said to have uniform velocity if it covers equal distance in equal intervals of time in a particular direction.

• Option 1 is the correct answer.
• As we know that tobacco consumption is harmful to health.
• The argument I is strong because it talks about the effects of the sale of tobacco products is restricted.
• The effect is valid, practical, and desirable for society as well. Argument II is weak because tobacco being harmful to us, we should not make its consumption more convenient.
• So, argument II to make tobacco purchases convenient is a weak argument.

Formula used:

Area of square = (side)²

Area of circle = π(radius)²

Calculation:

Radius of circle = 14/2 = 7 cm 

Required area = Area of the square - Area of a circle

Required area = (14)²- (22/7)(7)²  

Required area = 196 - 154 = 42 cm²

∴ Area of the square excluding the area occupied by the circle is 42 cm²

According to the given information :

Thus, Ankur is at a distance of 10 m from his home.

Hence, the correct answer is "10 m".

Concept:

When two bodies run in the opposite direction, then their relative velocities get added.

1 km/hr = 5/18 m/s.

1 m/s = 18/5 km/hr.

Calculation:

Length of train = 220 m, Speed of train = 54 km/hr ⇒ 15 m/s and Speed of man = 12 km/hr ⇒ 10/3 m/s [ 1 km/hr = 5/18 m/s]

\(Time = \frac{Distance}{Speed}\)

⇒ \(\frac{220}{\frac{10}{3}\;+\;15} \)   -----(Speed gets added due to different direction)

\(⇒ \frac{220\;\times\;3}{55}\)

⇒ 12 sec.

The correct answer is 1982.

Key Points

• The Directorate of Horticulture and Farm Forestry was established under the Department of Agriculture, Government of Madhya Pradesh, in the year 1982.
• This establishment aimed to enhance the state's horticulture development and promote farm forestry initiatives.
• It plays a crucial role in the implementation of various schemes and programs related to horticulture and farm forestry in Madhya Pradesh.
• The Directorate is also responsible for providing technical guidance and financial assistance to farmers for the cultivation of fruits, vegetables, and other horticultural crops.

Additional Information

• Horticulture Development in India
• Horticulture contributes significantly to the Indian agricultural economy by providing diverse products like fruits, vegetables, flowers, and spices.
• The National Horticulture Mission (NHM) is one of the major initiatives by the Government of India to promote horticulture development.
• It aims to enhance horticulture production, improve nutritional security, and increase income support to farm households.
• Horticultural crops are important for providing raw materials for the food processing industry.
• Farm Forestry
• Farm forestry involves the practice of growing trees on farmland to meet the needs of wood, fuel, and other forest products while providing environmental benefits.
• It helps in reducing pressure on natural forests and contributes to the sustainability of agricultural lands.
• Farm forestry initiatives are supported by various government schemes and subsidies to encourage farmers to adopt tree planting.
• It also plays a role in carbon sequestration, thereby contributing to climate change mitigation efforts.
• Agricultural Schemes in Madhya Pradesh
• The government of Madhya Pradesh has launched several schemes to support agriculture, including the Mukhyamantri Khet-Tirth Yojana and the Samagra Gram Vikas Yojana.
• These schemes focus on improving irrigation facilities, providing quality seeds, and offering financial assistance to farmers.
• They aim to enhance agricultural productivity and ensure sustainable development of rural areas.
• Role of the Directorate of Horticulture
• The Directorate of Horticulture plays a pivotal role in planning and executing horticulture development programs.
• It collaborates with various research institutions, universities, and extension agencies to provide updated knowledge and technologies to farmers.
• The Directorate also focuses on promoting organic farming practices and the use of modern agricultural techniques.

The correct answer is ​Total internal reflection.

Key Points

• Total internal reflection
• It is the complete reflection of a ray of light within a medium such as water or glass from the surrounding surfaces back into the medium.
• The phenomenon occurs if the angle of incidence is greater than a certain limiting angle, called the critical angle.
• Examples -
• The formation of a mirage.
• Shining of an empty test tube in water.
• Shining of a crack in a glass vessel.
• Sparkling of a diamond.
• Transmission of light rays in an optical fibre.

Additional Information

• Dispersion
• Dispersion is defined as the spreading of white light into its full spectrum of wavelengths.
• Examples - 
• Rainbow formation,
• Petrol poured on the water will show different colours,
• The prism splits the light into different colours on passing through it,
• Dispersion of colours in soap bubbles, etc.
• Diffraction
• Diffraction is the spreading of waves around obstacles.
• Examples - 
• X-Ray Diffraction,
• Water passing from a small gap,
• Solar or lunar corona, sound, etc.
• Reflection
• Reflection occurs when a light ray hits a surface and bounces off and returns to the medium from which it originated.
• Examples - 
• Reflection of light in the mirror, in a water pool, glowing stars, lighting of the moon at night, etc.

The logic here is: (square of Second number x 2) + 2 = First number

The number given 

52 : 5 ⇒ \((5^2\times 2)+2 = 52\)

100 : 7 ⇒ \((7^2\times 2)+2 = 100\)

Similarly,

? : 6 ⇒ \((6^2\times 2)+2 = 74\)

Thus, the missing number is 74.

Hence, the correct answer is "option (4)".

Shortcut Trick

Monthly Income = (Total Yearly Expenditure + Yearly Savings) ÷ 12

Total Yearly Expenditure = (4 × 2300) + (8 × 1800) = 9200 + 14400 = Rs. 23,600

Total Yearly Income = 23,600 + 12,400 = Rs. 36,000

Monthly Income = 36,000 ÷ 12 = Rs. 3,000

∴ The correct answer is Rs. 3,000.

Alternate Method

Given:

Average expenditure for first 4 months = Rs. 2,300

Average expenditure for next 8 months = Rs. 1,800

Total annual savings = Rs. 12,400

Formula Used:

Total Income = Total Expenditure + Total Savings

Monthly Income = Total Annual Income ÷ 12

⇒ Total Expenditure for first 4 months = 4 × 2300 = Rs. 9,200

⇒ Total Expenditure for next 8 months = 8 × 1800 = Rs. 14,400

⇒ Total Annual Expenditure = 9,200 + 14,400 = Rs. 23,600

⇒ Total Annual Income = Annual Expenditure + Annual Savings

⇒ Total Annual Income = 23,600 + 12,400 = Rs. 36,000

⇒ Monthly Income = 36,000 ÷ 12 = Rs. 3,000

∴ The correct answer is Rs. 3,000.

Additional Information

Income and Expenditure Relationship

The fundamental relation is Income = Expenditure + Savings. Any change in one parameter directly affects the others when the third is constant.

Weighted Average

When calculating average for different periods, use the weighted average formula: Avg = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n represents the number of months.

Unit Consistency

Always ensure the time periods match. If savings are given annually, convert expenditures to an annual sum before calculating monthly income.

The correct answer is Option 4 : Request the officer in charge to reconsider his decision.

• Qualities Projected in this situation:  (Effective intelligence, Speed of decision, Initiative, Sense of responsibility, Determination, and Courage).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Shortcut Trick

Apply the Successive Percentage Change formula: Net % Change = a + b + (a × b)/100

Here, Increase (a) = +15% and Decrease (b) = −12%

Net % Change = 15 − 12 + (15 × −12)/100

Net % Change = 3 − 180/100 = 3 − 1.8 = 1.2%

Since the result is positive, it is an effective increase.

∴ The correct answer is 1.2%.

Alternate Method

Given:

Initial Price Increase = 15%

Subsequent Price Decrease = 12%

Calculations:

⇒ Let the Initial Price of the item be 100 units.

⇒ Price after 15% increase = 100 + (15% of 100) = 115 units.

⇒ Price after 12% decrease = 115 − (12% of 115)

⇒ 12% of 115 = (12 × 115)/100 = 1380/100 = 13.8 units.

⇒ Final Price = 115 − 13.8 = 101.2 units.

⇒ Effective Increase = Final Price − Initial Price = 101.2 − 100 = 1.2 units.

⇒ Effective Percentage Increase = (1.2/100) × 100 = 1.2%.

∴ The correct answer is 1.2%.

Additional Information

Successive Percentage Formula

For two successive changes of x% and y%, the net change is given by [x + y + (xy/100)]%. Use positive for increase and negative for decrease.

Multiplying Factor Method

Final Value = Initial Value × (1 + x/100) × (1 + y/100). For 15% increase and 12% decrease, factor = 1.15 × 0.88 = 1.012.

Percentage Change vs. Percentage Point

Percentage change measures the relative change, while percentage point measures the arithmetic difference between two percentages.

The correct answer is 99^th constitutional amendment act.

The 99^th constitutional amendment act 2014 or National Judicial appointment commission have replaced the collegiums system of appointing judges to the Supreme Court and high courts. It created the new body called the National Judicial Appointment Commission.

History:

• First Judge Case in 1982, the Supreme Court held that consultation does not mean concurrence and it only applies the exchange of views.
• Second Judge Case 1993, the court reversed earlier ruling and changed the meaning of consultation to concurrence. It implies that the advice given by the Chief Justice of India to President in the matter of appointment of the judges is binding.
• Third Judge Case 1998, the court said that advice given by Chief Justice of India should not be sole opinion but the consultation of the plurality of judges. He should consult a collegium of four senior-most judges and if two are in an opposite opinion he should not send the recommendation.
• 99^th constitutional amendment act 2014 created the National Judicial Appointment Commission.
• In 2015, the Supreme Court has declared 99^th constitutional amendment act and National Judicial Appointment Commission unconstitutional and void. This was the Fourth Judge Case. The court said that the new system would affect the independence of the judiciary.
• After that earlier collegiums system came into operation again.

The correct answer is Ag.

• Compounds of Ag are used in black and white photography.

Key Points

• Silver:
• Symbol: Ag (Latin word: Argentums)
• Atomic mass: 107.8682 u
• Atomic number: 47
• The compounds of Silver(Ag), silver bromide and silver chloride are used in black and white photography.
• These two are photosensitive compounds.
• They get easily decomposed on exposure to light.
• Hence, they are used in black and white photography and films.

Additional Information

According to the given information:

Eight boys A, B, C, D, E, F, G and H are sitting in a row facing towards the south.

A and H are at extreme ends of the row.

E and F are immediate neighbours of B.

C is fourth to the left of B.

F is to the immediate left of A.

D is not the immediate neighbour of C.

Thus, B is sitting on the immediate left of F.

Hence, the correct answer is "B".

Shortcut Trick

Reduce the angle 630° by subtracting the nearest multiple of 360°.

sin(630° + A) = sin(360° + 270° + A) = sin(270° + A).

Using the Allied Angle rule, sin(270° + A) = −cos A.

Expression: −cos A + cos A = 0.

∴ The correct answer is 0.

Alternate Method

Given: sin(630° + A) + cos A

Formula Used: sin(n × 360° + θ) = sin θ and sin(270° + θ) = −cos θ

⇒ sin(630° + A) = sin(360° + 270° + A)

⇒ sin(270° + A)

⇒ sin(3 × 90° + A)

⇒ −cos A [Since (270° + A) lies in the 4^th quadrant where sine is negative]

⇒ Expression = −cos A + cos A

⇒ 0

∴ The correct answer is 0.

Additional Information

Allied Angles Rule (ASTC)

In the 4^th quadrant (270° to 360°), only Cosine and Secant are positive. Sine, Tangent, Cotangent, and Cosecant are negative.

Trigonometric Function Change

Functions change at (90° ± θ) and (270° ± θ): sin → cos, tan → cot, sec → cosec. They remain the same at (180° ± θ) and (360° ± θ).

Periodicity of Sine and Cosine

The values of sin θ and cos θ repeat every 360° (or 2π radians). Thus, sin(n × 360° + θ) = sin θ for any integer n.

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week, starting from Monday and ending on Sunday of the same week.

1) S has the exam on Thursday.

2) Only one person has the exam between S and V. 

3) Q has the exam on the day immediately before V but not on a Monday. 

4) Only two people have exams between Q and U.

5. P's exam is on one of the days before T but on one of the days after R.

Thus, according to the final arrangement R has exam on Monday.

Hence, "Option 4" is the correct answer.

Concept used:

Calculation:

325 + 276 ÷ [150 − {9 × 9 + (83 − 4 × 15)}]

⇒ 325 + 276 ÷ [150 − {9 × 9 + 23}]

⇒ 325 + 276 ÷ [150 − 104]

⇒ 325 + 276 ÷ 46

⇒ 325 + 6 = 331

The correct answer is option 1.

Key Points

• The citadel in Harappan cities was a raised area where public buildings and possibly religious structures were located. Hence, option 1 is correct.
• Important Fact: The citadel was an elevated platform, distinct from the lower town where most residents lived.

An endothermic reaction is a reaction in which heat is absorbed.

An exothermic reaction is a reaction in which heat is released.

Given

Statements:

Some tables are green.

All green is lawn.

All lawn is soft.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All tables are green - False (Because, Some tables are green).

II. Some green is lawn - True (Because, All green is lawn also implies that Some green is lawn).

So, Only conclusion II follows.

Hence, the correct answer is "Option 2".

Shortcut Trick

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k

Here, k = 2√2

Required value = (2√2)³ + 3 × (2√2)

⇒ 16√2 + 6√2 = 22√2

∴ The correct answer is 22√2.

Alternate Method

Given:

x − 1/x = 2√2

Formula Used:

(a − b)³ = a³ − b³ − 3ab(a − b)

Calculations:

⇒ a³ − b³ = (a − b)³ + 3ab(a − b)

Substitute a = x and b = 1/x into the formula:

⇒ x³ − 1/x³ = (x − 1/x)³ + 3 × x × (1/x) × (x − 1/x)

⇒ x³ − 1/x³ = (x − 1/x)³ + 3(x − 1/x)

Put the given value of (x − 1/x) = 2√2:

⇒ x³ − 1/x³ = (2√2)³ + 3 × 2√2

⇒ (2√2)³ = 2³ × (√2)³ = 8 × 2√2 = 16√2

⇒ x³ − 1/x³ = 16√2 + 6√2

⇒ x³ − 1/x³ = 22√2

∴ The correct answer is 22√2.

Additional Information

Sum of Cubes Identity

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Sum of Squares Identities

If x + 1/x = k, then x² + 1/x² = k² − 2. Conversely, if x − 1/x = k, then x² + 1/x² = k² + 2.

Sign Conversion Rules

If x + 1/x = k, then x − 1/x = √(k² − 4). Similarly, if x − 1/x = k, then x + 1/x = √(k² + 4).

Interchanging the signs in the equation according to the options and solving each option according to “BODMAS” rule.

Option (1): × and +

4 + 8 x 7 + 9 ÷ 60 - 5 = 83

4 + 8 × 7 + 0.15 - 5 = 83

4 + 56 + 0.15 - 5 = 83

60.15 - 5 = 83

55.15 ≠ 83

Option (2): × and -

4 - 8 + 7 - 9 ÷ 60 × 5 = 83

4 -8 + 7 - 0.15 × 5 = 83

4 - 8 + 7 - 0.75 = 83

4 - 15 - 0.75 = 83

-11.75 ≠ 83

Option (3): × and ÷

4 ÷ 8 + 7 ÷ 9 × 60 - 5 = 83

0.5 + 0.778 × 60 - 5 = 83

0.5 + 46.67 - 5 = 83

47.17 - 5 = 83

42.17 ≠ 83

Option (4): - and ÷

4 × 8 + 7 × 9 - 60 ÷ 5 = 83

4 × 8 + 7 × 9 - 12 = 83

32 + 63 - 12 = 83

95 - 12 = 83

83 = 83

Hence, Option (4) is correct answer.

Given : 

Average of 8 numbers is 18.

One of the numbers is excluded, the average becomes 20.

Formula Used : 

Average =  Sum of all observations/Number of observations

Calculation : 

Sum of 8 numbers = 18 × 8 = 144

Sum of 7 numbers = 20 × 7 = 140

Excluded number = 144 - 140 = 4

∴ The correct answer is 4.

The correct answer is Vindhyachal.

Key Points

• Vindhyachal Mountain
• It is the oldest mountain series of the state and is situated in the middle of Madhya Pradesh.
• Highest Peak - The Sadbhawna Shikhar or the "Goodwill Peak".
• Its easternmost Hill is Kaimur and westernmost is Kakrabardi hills.
• Composition - Redstone, Quartz, and Silica.
• Situated Northern side of the Narmada river.
• Extension - West to Eastern Madhya Pradesh, Chhattisgarh, Bihar.
• Districts in Madhya Pradesh - Bhopal, Raisen, Sehore, Dhar, Damoh, Katni, Shandol.
• Soil - Black and Mountainous Soil.
• Rivers - Ken, Tons, Betwa.
• Average Rainfall -125 cm.
• Forest - Mainly Teak and Tendu.
• Minerals - Lime Stone, Coal, Geru.
• Industrial Areas - Pithampur (Dhar), Mandeep (Raisen), Bhopal.
• Major Crops - Gram, Wheat, Soyabean.
• Tourists spots - Amarkantak,Bhimbethka,Sanchi.

The correct answer is Yellow and blue

• Yellow and blue combination of color is the most convenient during the day and night time.

Key Points

• The modern color theory is also known as the RGB color model which is red, green, and blue are additive primary colors.
• A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light.
• When we look towards the sun at sunset, we see red and orange colors because the blue light has been scattered out and away from the line of sight.
• Blue, Red, and green, light combined together make white light, and these three colors, combined in different mixtures, can produce almost any color.
• This is the principle used to make the colors on television and computer screens.

Six friend facing west: Gaurav,meenal,Varun, Vasu, Lalit, Poorvi

1. Gaurav is sitting at one of the corners

2. Gaurav is sitting at the third place to the left of Meenal.

.

3. Lalit is sitting to the immediate right of Meenal.

4. Varun is sitting between Vasu and Meenal.

5. Poorvi is third to the right of Varun.

Hence, “Lalit” is sitting to the immediate left of Poorvi.

GIVEN:

A pyramid has a square base with side 12 cm and the height of the pyramid is 14 cm.

FORMULA USED:

Volume of pyramid = 1/3 × Area of base × Height

CALCULATION:

Applying the formula:

Area of the square base = 12 × 12 = 144 cm²

Height of pyramid = 14 cm

∴ Volume of pyramid = (1/3) × 144 × 14 = 672 cm³

According to the given information,

Code for "sut" is tea.

Code for "has" is coffee.

Code for "lim" is And.

Code for 'lew" is either Is or Bringing.

Code for 'ploy' is either Is or Bringing.

Now, we left with only "wir" and it's code is "he".

Hence, the correct answer is "wir".

Shortcut Trick

Let the Cost Price (CP) be x.

Successive multipliers: 1.12 (Manufacturer) × 1.10 (Wholesaler) × 1.15 (Retailer).

x × (112 ÷ 100) × (110 ÷ 100) × (115 ÷ 100) = 56,672

x × (28 ÷ 25) × (11 ÷ 10) × (23 ÷ 20) = 56,672

x × (7084 ÷ 5000) = 56,672

x = (56,672 × 5000) ÷ 7084 = 8 × 5000 = 40,000

∴ The correct answer is ₹40,000.

Alternate Method

Given: Retail Price = ₹56,672, Manufacturer Gain = 12%, Wholesaler Gain = 10%, Retailer Gain = 15%.

Formulas: SP = CP × (100 + Gain%) ÷ 100

⇒ Let CP = x

⇒ Price after Manufacturer = x × 1.12

⇒ Price after Wholesaler = (x × 1.12) × 1.10

⇒ Price after Retailer = (x × 1.12 × 1.10) × 1.15 = 56,672

⇒ x × 1.4168 = 56,672

⇒ x = 56,672 ÷ 1.4168 = 40,000

∴ The correct answer is ₹40,000.

Additional Information

Successive Percentage Change

When multiple profit percentages are applied one after another, the final price is calculated using the product of their multipliers: Final = Initial × (1 + r₁) × (1 + r₂) × (1 + r₃).

Chain Rule in Profit and Loss

The Selling Price (SP) for one person in the chain becomes the Cost Price (CP) for the next person.

The correct answer is 2003.

Key Points

• Burhanpur District was created on 15 August 2003, from the southern portion of Khandwa District.
• The district is divided from Khandwa District on the north by the Satpura Range.
• The district was historically part of the Nimar and Khandesh regions.
• During the rise of Buddhism, the region was part of Avanti.

Additional Information

• Madhya Pradesh is known as the “Heart of India” as it has been home to the cultural and spiritual heritage of almost all religions.
• At present Madhya Pradesh consists of 10 divisions and 52 districts.
• Bhopal is the capital of Madhya Pradesh.

• A calorimeter is used to measure the enthalpy, the heat energy, of a reaction.
• A thermometer is an instrument for measuring temperature. It usually consists of a narrow glass tube containing a thin column of a liquid which rises and falls as the temperature rises and falls.
• A pyrometer is an apparatus for measuring high temperatures that uses the radiation emitted by a hot body as a basis for measurement.
• A thermocouple is a device for measuring temperature consisting of a pair of wires of different metals or semiconductors joined at both ends. One junction is at the temperature to be measured, the second at a fixed temperature. The electromotive force generated depends upon the temperature difference

The correct answer is Option 4: Not pay any attention to the allegations and continue your work.

• Qualities Projected in this situation:  (Effective Intelligence, Self-confidence, Courage, Presence of mind, and Speed of decision making).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Shortcut Trick

For any sequence of consecutive even or odd numbers, the numbers form an Arithmetic Progression (AP).

In an AP, the average of all terms is equal to the average of the first and last terms.

⇒ Average = (Smallest Number + Largest Number) ÷ 2

⇒ Smallest + Largest = 2 × Average

⇒ Sum = 2 × 35 = 70

∴ The correct answer is 70.

Alternate Method

Given:

Average of 6 consecutive even numbers = 35

Formula Used:

Average = Sum of observations ÷ Number of observations

30
Smallest

32

34

36

38

40
Largest

Avg = 35

Sum = 30 + 40 = 70

Calculations:

⇒ Let the 6 consecutive even numbers be x, x + 2, x + 4, x + 6, x + 8, and x + 10.

⇒ Sum of these 6 numbers = x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10)

⇒ Sum = 6x + 30

⇒ Average = (6x + 30) ÷ 6 = x + 5

⇒ We are given that the average is 35.

⇒ x + 5 = 35

⇒ x = 35 − 5 = 30

⇒ The smallest number = x = 30

⇒ The largest number = x + 10 = 30 + 10 = 40

⇒ Sum of smallest and largest number = 30 + 40 = 70

∴ The correct answer is 70.

Additional Information

Average of an Arithmetic Progression (AP)

For any sequence with a constant difference (like consecutive numbers), the average is simply (First Term + Last Term) ÷ 2.

Consecutive Even/Odd Numbers

Any sequence of consecutive even or odd numbers has a common difference of 2. For n numbers, the difference between the largest and smallest term is exactly 2 × (n − 1).

Sum of 'n' terms in AP

The total sum of terms in an arithmetic sequence can be calculated quickly as: Sum = n × Average.

Option1 : E - 2 = C; C - 2 = A

Option2 : Q - 2 = O; O - 2 = M

Option3 : G + 2 = I; I + 2 = K

Option4 : V - 2 = T; T - 2 = R

Hence, GIK is the odd cluster of letters.

Formula used:

sin²ø + cos²ø = 1

sin (90 - ø) = cos ø

cos (90 - ø) = sin ø 

Calculation:

sin 35° cos 55° + cos 35° sin 55°

In the given expression we can write 35 as (90 - 55)

⇒ sin (90 - 55)° cos 55° + cos (90 - 55)° sin 55°

By using the formula, sin ( 90 - ø ) = cos ø and cos ( 90 - ø) = sin ø 

⇒ cos 55° cos 55° + sin 55° sin 55°

⇒ cos² 55° + sin² 55°

⇒ cos2 55° + sin2 55° = 1 (by formula  sin2ø + cos2ø = 1)

The value of the expression is 1

Key Points

Ajanta Caves-

• The Ajanta Caves are a series of 29 Buddhist cave temples in Ajanta, India, some of which date from the 2^nd century BC. Encompassing both Theravada and Mahayana Buddhist traditions, the Ajanta caves preserve some of the best masterpieces of Buddhist art in India.
• Out of 29, 25 caves were used as Viharas or residential caves while 4 were used as Chaitya or prayer hills.
• It is said that Buddhist monks lived, studied and prayed in Ajanta caves for a long time.
• The Ajanta Caves were carved in the 2^nd century BC out of a horseshoe-shaped cliff along the Waghora River.
• The caves were designated a UNESCO World Heritage site in 1983.

Ellora caves- 

• The Ellora caves, locally known as 'Verul Leni' is located on the Aurangabad - Chalisgaon road at a distance of 30 km north - northwest of Aurangabad, in the Indian state of Maharashtra.
• Ellora is one of the largest rock-cut monastery - temple caves complexes in the world, and a UNESCO World Heritage Site.
• The cave temples and monasteries at Ellora, excavated out of the vertical face of an escarpment, are 26 km north of Aurangabad.
• Sculptors, inspired by Buddhism, Jainism and Hinduism, created elaborate rock carvings. Extending in a linear arrangement, the 34 caves contain Buddhist Chaityas or halls of worship, Viharas or monasteries and Hindu and Jain temples.
• Spanning a period of about 600 years between the 5^th and 11^th century A.D., the earliest excavation here is of the Dhumar Lena (Cave 29).
• The Kailasha temple features the largest single monolithic rock excavation in the world.
• During the regime of the Rashtrakuta were the famous Ellora caves of Maharashtra built.

Extra facts:

• Madhya Pradesh- Bagh Caves
• Maharashtra - Ajanta Caves, Bhaja Caves, Elephanta Caves, Ellora Caves, Kanheri Caves
• Karnataka- Badami Caves
• Bihar - Barabar Caves
• Madhya Pradesh- Udaygiri Caves
• Andhra Pradesh - Borra Caves
• Tamilnadu - Varah Caves

The correct answer is Diaphragm**.**

Key Points

• A large, muscular sheet called a diaphragm forms the floor of the chest cavity.
• The diaphragm, located below the lungs, is the major muscle of respiration.
• It is a large, dome-shaped muscle that contracts rhythmically and continually, and most of the time, involuntarily.
• Upon inhalation, the diaphragm contracts and flattens and the chest cavity enlarges.

Additional Information

• Duodenum - The first part of the small intestine. It connects to the stomach. The duodenum helps to further digest food coming from the stomach. It absorbs nutrients (vitamins, minerals, carbohydrates, fats, proteins) and water from food so they can be used by the body.
• The larynx is a hollow tube that connects your throat (pharynx) to the rest of your respiratory system. It helps you swallow safely and contains the vocal cords, so it's often called the voice box.
• The alveoli are where the lungs and the blood exchange oxygen and carbon dioxide during the process of breathing in and breathing out. Oxygen breathed in from the air passes through the alveoli and into the blood and travels to the tissues throughout the body.

The pattern followed here is,

First letter of each word:

I + 1 = J; J + 1 = K; K + 1 = L; L + 1 = M

Second letter of each word:

M + 2 = O; O + 2 = Q; Q + 2 = S; S + 2 = U

Hence, MU is the correct answer.

Given:

The polynomial = 3x3 - 7x2 + kx + 12 

The polynomial is divisible by (x - 3)

Concept used:

If polynomial P(x) is divided by x - a, then remainder is P(a).

If the remainder P(a) is 0, then P(x) is divisible by x - a.

Calculation:

Here, P(x) = 3x3 - 7x2 + kx + 12

If x - 3 = 0 then x = 3

So, remainder = k(3)

But according to the question, k(3) = 0

⇒ 3 × 33 - 7 × 32 + k × 3 + 12 = 0

⇒ 81 - 63 + 3k + 12 = 0

⇒ k = - 10

∴ The value of K is - 10.

Statements:

Some buses are motorbikes.

All motorbikes are vans.

All buses are cars.

The Venn diagram as per the given

Statements:

Conclusions:

(I) Some cars are vans. → True (Because all buses are cars, some buses are motorbikes and all motorbikes are vans, which means some cars are vans is definitely true)

(II) Some vans are buses. → True (Because some buses are motorbikes and all motorbikes are vans, which means some vans are buses is definitely true)

(III) Some vans are motorbikes. → True (Because all motorbikes are vans, which means some vans are motorbikes is definitely true)

Hence, the correct answer is "All conclusions I, II and III follow".

Shortcut Trick

Apply the direct algebraic identity: x² + y² = (x + y)² − 2xy

Substitute the given sum (15) and product (45):

Value = 15² − 2 × 45 = 225 − 90

Value = 135

∴ The correct answer is 135.

Alternate Method

Given:

Sum of variables (x + y) = 15

Product of variables (xy) = 45

Formula Used:

Standard expansion of a binomial square: (x + y)² = x² + y² + 2xy

Calculations:

⇒ (15)² = x² + y² + 2 × 45

⇒ 225 = x² + y² + 90

⇒ x² + y² = 225 − 90

⇒ x² + y² = 135

∴ The correct answer is 135.

Additional Information

Square of Difference Identity

The identity for the square of a difference is (x − y)² = x² + y² − 2xy. It can also be expressed as (x − y)² = (x + y)² − 4xy.

Sum and Difference of Cubes

Related higher-power identities include x³ + y³ = (x + y)(x² − xy + y²) and x³ − y³ = (x − y)(x² + xy + y²).

Product and Sum Relation

The value of x² + y² is always non-negative for real numbers x and y, which implies (x + y)² ≥ 2xy.

The correct answer is Second.

In News

• India has achieved the rank of second-largest National Highway network globally, following a 60% growth in the past decade.

Key Points

• The National Highway network expanded from 91,287 km in 2014 to 146,195 km in 2024.
• Top rank: United States
• High-speed corridors have surged from 93 km to 2,474 km.
• India’s highway development contributes to enhanced connectivity, trade, and logistics efficiency.
• Significant investments and initiatives like Bharatmala Pariyojana have driven this growth.

Additional Information

• India's National Highway Growth
• Ranked second globally, reflecting significant development over the past decade.
• Projects under Bharatmala Pariyojana and Port Connectivity Masterplan have contributed to this milestone.
• Bharatmala Pariyojana
• Aims to improve road infrastructure and establish multimodal logistics parks.
• Plans to handle 700 million metric tonnes of cargo annually through its logistics network.
• Technological Initiatives
• FASTag system has improved toll collection efficiency with over 10.1 crore issued.
• The e-Transport project centralized transport services for better management.

• The correct answer is option 4, i.e., Zinc is more reactive than tin.
• Food cans are coated with tin and NOT zinc because zinc is more reactive than tin.
• Zinc being more reactive, it reacts with the organic acids present in the food. Due to this it can get dissolved in the food substance and make the food poisonous.
• It is due to this reason that tin, a less reactive metal is used.

Given: 

UVW's rank from the top = 21^st

UVW's rank from the bottom = 64^th

Total number of students = UVW's rank from the top + UVW's rank from the bottom - 1

(21 + 64) - 1 = 85 - 1 = 84

Hence, the total number of students is "84".

Given:

Marked Price (MP) = ₹3,675

Discount = 12%

Loss = 2%

Formula used:

Selling Price (SP) = MP - (Discount% × MP)

Cost Price (CP) = \(\dfrac{SP}{(1 - \frac{Loss%}{100})}\)

Calculation:

SP = 3675 - (12% × 3675)

⇒ SP = 3675 - (0.12 × 3675)

⇒ SP = 3675 - 441

⇒ SP = 3234

CP = \(\dfrac{3234}{(1 - \frac{2}{100})}\)

⇒ CP = \(\dfrac{3234}{0.98}\)

⇒ CP = 3300

∴ The correct answer is option 2.

The logic followed here is:

Hence, '48' is the correct answer.

Shortcut Trick

Total time for the journey = 750 ÷ 50 = 15 hours.

Time spent on the first 200 km = 200 ÷ 40 = 5 hours.

Remaining time for the next 550 km = 15 − 5 = 10 hours.

Required speed for remaining distance = 550 ÷ 10 = 55 kmph.

∴ The correct answer is 55 kmph.

Alternate Method

Given:

Total distance = 750 km

Distance of 1^st part = 200 km, Speed of 1^st part = 40 kmph

Distance of 2^nd part = 550 km

Overall average speed = 50 kmph

Formula Used:

Average Speed = Total Distance ÷ Total Time

Speed = Distance ÷ Time

200 km
550 km
Total Distance: 750 km (Avg Speed: 50 kmph)

Speed = 40 kmph
Time = 5 hrs

Speed = ? kmph
Time = 10 hrs

Calculations:

⇒ Total Time = Total Distance ÷ Average Speed

⇒ Total Time = 750 ÷ 50 = 15 hours

⇒ Time taken for the first 200 km = Distance ÷ Speed = 200 ÷ 40 = 5 hours

⇒ Time remaining for the next 550 km = Total Time − Time taken for the first part

⇒ Time remaining = 15 − 5 = 10 hours

⇒ Required speed for the next 550 km = Distance ÷ Time

⇒ Required speed = 550 ÷ 10 = 55 kmph

∴ The correct answer is 55 kmph.

Additional Information

Average Speed

Average speed is the total distance traveled divided by the total time taken. It is not simply the arithmetic mean of the different speeds.

Average Speed for Equal Distances

If an object covers two equal distances at speeds x and y, the average speed over the entire journey is directly calculated using the formula 2xy ÷ (x + y).

Relative Speed

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. When moving in the same direction, it is the difference between their individual speeds.

The correct answer is Aravalli.

• Sabarmati River:
• The Sabarmati basin extends over the states of Rajasthan and Gujarat having an area of 21,674 Sq.km with a maximum length and width of 300 km and 150 km.
• It lies between 70°58’ to 73°51’ east longitudes and 22°15’ to 24°47’ north latitudes.
• Sabarmati river originates from the Aravalli hills in Kotdi tehsil of Udaipur district of Rajasthan.
• The basin is bounded by Aravalli hills on the north and north-east, by Rann of Kutch on the west and by the Gulf of Khambhat on the south.
• The basin is roughly triangular in shape with the Sabarmati River as the base and the source of the Vatrak River as the apex point.
• Sabarmati originates from Aravalli hills at an elevation of 762 m near village Tepur, in the Udaipur district of Rajasthan.
• Right Bank Tributaries: Sei, Siri and Dhamni
• Left Bank Tributaries: Wakal, Harnav, Hathmati, Khari, Watrak.

The correct answer is poisons.

• Catalytic poisons are those substances that themselves are not catalysts but whose presence decreases the activity of the catalyst.
• This occurs due to preferential adsorption of poison on the surface of the catalyst.
• They are also known as anti catalysts or catalyst inhibitors.

​Catalyst:

• It is a substance that increases the rate of a reaction without taking a direct part in the reaction.
• Catalysts do not undergo chemical change in themselves.
• When we need to control the rate of reaction which has increased due to the addition of a catalyst, catalytic poisons are added.

Additional Information

Promoter

• It is a substance added to a solid catalyst to improve its performance in a chemical reaction.
• The promoter itself has little or no catalytic effect.

Initiators

• Initiators are substances that help to initiate (start) a chemical reaction.

Controllers

• Controllers are used for controlling the rate of a chemical reaction.
• They can be mechanical, thermal, or chemical in nature.

According to the English alphabet series and its positional value:

The pattern followed here is:

Thus, instead of ‘SH’ it should be ‘SG’.

Given:

a + b + c = 2

ab + bc + ca.= -1

Concept used:

a3 + b3 + c3 - 3abc = (a + b + c)( a2 + b2 + c2 – ab – bc – ca)

Calculation:

a² + b² + c² + 2(ab + bc + ca) = 4 

⇒ a2 + b2 + c2 - 2 = 4 

⇒ a2 + b2 + c2 = 6 

Now,

a3 + b3 + c3 - 3abc = 2 {6 – (- 1)}

⇒ 14

∴ Required answer is 14

We will use the following table for the tree diagram,

Hence, man is the father in law of women.

Given:

Principal (P) = ₹800

Amount (A) = ₹926.10

Rate (r) = 10% per annum compounded half-yearly ⇒ 5% per half-year

Formula used:

A = P\((1+\frac{r}{100})^n\)

Where, n = number of half-years

Calculation:

926.10 = 800\((1+\frac{5}{100})^n\)

⇒ \(\frac{926.10}{800}= (1+\frac{5}{100})^n\)

⇒ \(1.157625 = (1.05)^n\)

Check powers of 1.05:

1.05¹ = 1.05

1.05² = 1.1025

1.05³ = 1.157625

⇒ n = 3 half-years

Time (t) = \(\frac{3}{2} \) = \(1 \frac{1}{2}\) years

∴ The correct answer is \(1 \frac{1}{2}\) years

The correct answer is Option 2.

Key Points

• The Indian government set up the Shah Commission under the chairmanship of Justice JC Shah on 23 April 1966 to divide the existing state of Punjab and determine the boundaries of the new state of Haryana after consideration of the languages spoken by the people.
• The commission delivered its report on 31 May 1966 whereby the then-districts of Hisar, Mahendragarh, Gurgaon, Rohtak and Karnal were to be a part of the new state of Haryana.
• Hence option 2 is correct.

Additional Information

• The foundation of HPSC was led on 1 November 1966 when Haryana state was formed after the independence movement of India.
• It was originally established under the provisions of the Punjab Reorganisation Act, 1966.
• Government of India Act 1935 authorized the state government to form a state public service commission.

• Nitre or Salt peter (KNO₃) is an ore of Potassium (K).
• Magnesite(MgCO3) , Dolomite(CaMg(CO3)₂ and Epsom Salt (MgSO4) are ores of Magnesium.
• Ore is a naturally occurring mineral or rock from which metal can be extracted.

The logic followed here is:

Logic: (1^st number × 3) + 3 = 2^nd number.

Now,

For, 40 : 123

⇒ (40 × 3) + 3

⇒ 120 + 3 = 123.

For, 63 : 192

⇒ (63 × 3) + 3 

⇒ 189 + 3 = 192.

Similarly, for 39 : 120

⇒ (39 × 3) + 3

⇒ 117 + 3 = 120.

Hence, the correct answer is "Option 2".

Concept used:

Calculation:

18 ÷ {(6 of 2 - 4)} × 5(6 - 3)

⇒ 18 ÷ {(12 - 4)} × 5 × 3

⇒ 18 ÷ 8 × 5 × 3

⇒ (9/4) × 5 × 3

⇒ 135/4

∴ The correct answer is 135/4.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘ASVO’ is the correct answer.

Given:

Simple Interest (SI) = ₹1260

Rate₁ = 5% per annum

Time₁ = 9 years

Time₂ = 5 years

Formula used:

SI = \(\frac{P × R × T}{100}\)

Calculation:

1260 = \(\frac{P × 5 × 9}{100}\)

⇒ 1260 = \(\frac{45P}{100}\)

⇒ P = \(\frac{1260 × 100}{45} = 2800\)

Now use P = ₹2800, SI = ₹1260, T = 5 years

1260 = \(\frac{2800 × R × 5}{100}\)

⇒ 1260 = \(\frac{14000R}{100}\)

⇒ 1260 = 140R

⇒ R = \(\frac{1260}{140} = 9\)

∴ The correct answer is 9% per annum

The correct answer is Shivna.

Key Points

• Pashupatinath Temple
• The Mandsaur Shiva Temple, also known as the Pashupatinath Temple at Mandsaur, is a Hindu temple in Mandsaur, Madhya Pradesh, India.
• It is devoted to Lord Shiva.
• It is a part of the Pashupatinath tradition, one of the six main schools of Shaivism.
• It is noted for having an eight-faced Shiva Linga and is situated on the Shivna River.
• Based on inscriptions, the temple sculpture is dated to the fifth or sixth century.
• Some of the inscriptions refer to the location as Dashapura.

Additional Information

• The location has been crucial for dating and architectural research at some distant sites, including the Elephanta Caves.
• It is located in the historical region of Malwa, close to the Rajasthani border.
• It is about 200 kilometres (120 miles) from Indore, about 340 kilometres (210 miles) west of the Udaigiri Caves, and about 220 kilometres (140 miles) east of the Shamalaji ancient sites.
• The 4.5-meter (15-foot) tall eight-face Shiva statue is located at the Pashupatinath temple that has been rebuilt.

• The tendon is made up of dense fibrous connective tissue composed of primarily collagenous fibres.
• Primary collagenous fibres, which is made up of bunches of collagen fibrils.
• Collagen fibrils are the basic units of a tendon.
• Tendons occur at the end of skeletal muscles and serve to attach them strongly to bones.
• It is a modification of white fibrous tissue.

**Given

Statements:

**

I. X = Y = Z

II. Y > A ≥ B ≤ D

On combining, we get:

X = Z = Y > A ≥ B ≤ D

Conclusions:

I. X > B → True (As X = Z = Y > A ≥ B, it gives X > B)

II. X < D → False (As X = Z = Y > A ≥ B ≤ D, there is no direct relation between X and D. So, it can be possible but not definitely true.)

So, only conclusion I follows.

Hence, the correct answer is "Option 2".

Given:

Price increase = 25% = 1/4

Formula used:

To maintain the same expenditure, the reduction in consumption

⇒ 1/(Denominator - Numerator) × 100

Calculation:

Reduction in consumption = 1/(4 + 1) × 100 = 1/5 × 100 = 20%

∴ The consumption should be reduced by 20%

Alternate Method

⇒ p × m = nm × 1.25p

⇒ n = 0.8

⇒ Reduced consumption = (1 - 0.2) × 100 = 20%

∴ The consumption should be reduced by 20%

Position values of the letters, according to the English alphabet series is:

The logic followed for RKP : VHS is mentioned below-

Similarly, 

UJM will be written as-

Hence, "XHQ" is correct answer.

Given:

Ravi spends 70% of his income. His income increases by 25% and his expenditure also increases by 10%

Concept used:

Income - Expenses = Saving

Calculation:

Let the income be 100p

According to the question:

Ravi spends 70% of his income

Expenses = 70p

⇒ 100p - 70p = 30p

Savings = 30p

Income increases by 25% 

⇒ 100p + 25p = 125p

Expenditure increases by 10% 

⇒ 70p + 70p × 10/100 = 77p 

Savings = 125p - 77p = 48

Saving Increase% = (48 - 30)/30 × 100

= 60%

The answer is 60%

The correct answer is A Century is not enough.

Key Points

• "A Century is not enough" is an autobiography by Sourav Ganguly, one of India's most successful cricket captains.
• This book provides a deep insight into his cricket career, leadership, and personal life.
• It covers his journey from a young cricketer to becoming the captain of the Indian cricket team.
• The book also highlights his challenges, achievements, and the controversies he faced during his career.

Additional Information

The correct answer is Fermi.

Key Points

• Fermi is a unit of length used to measure nuclear distances, = 10⁻¹⁵ meters. Hence option 2 is correct.
• It is named for the Italian physicist Enrico Fermi (1901–1954).
• A fermi is equivalent to a femtometer and is the older non–SI measurement unit of length.
• Femtometer is a derived metric measurement unit of length.
• Since it is a typical length-scale, and often referenced in nuclear physics.

Additional Information

• Angstrom is the unit of length used to measure the wavelength of light, 1 Å = 10^-10 m.
• A light-year is the unit of length for measuring astronomical distances.
• Light year = distance traveled by light in 1 year = 9.4605 × 10¹⁵ m.
• Astronomical unit = Mean distance between the sun and earth = 1.5 × 10¹¹ m.
• Parsec = 3.26 light years = 3.084×10¹⁶ m.
• The barn is the unit of area for measuring scattering cross-section of collisions. 1 barn = 10^-28 m².
• Chronometers and metronomes are time-measuring instruments. The quantity having the same unit in all the systems of units is time.